The theory of finitary biframes as order-theoretical duals bitopological spaces is explored. category a coreflective subcategory that biframes. Some the advantages adopting pointfree notion bispaces are studied. In particular, it shown for every biframe there which plays role analogue to assembly in frames: L A(L) with universal property analogous frame; and such its main component isomorphic o...

In this paper, we first define soft u-open sets and s-open as two new classes of on bitopological spaces. We show that the class p-open lies strictly between these classes, give several sufficient conditions for equivalence each sets, respectively. addition to these, introduce u-?-open, p-?-open, s-?-open three in spaces, which contain Via notions Lindelöfeness SBTSs. discuss relationship notio...

We extend the path lifting property in homotopy theory for topological spaces to bitopological semigroups and we show and prove its role in the C(ℵ)-fibration property. We give and prove the relationship between the C(ℵ)-fibration property and an approximate fibration property. Furthermore, we study the pullback maps for C(ℵ)-fibrations.

The aim of this paper is to introduce the concepts of τ1τ2-regular generalized star star closed sets , τ1τ2-regular generalized star star open sets and study their basic properties in bitopological spaces. Keywords—τ1τ2-regular closed sets; τ1τ2-regular open sets; τ1τ2-regular generalized closed sets; τ1τ2-regular generalized star closed sets; τ1τ2-regular generalized star star closed sets.